An unconventional view of the `closest sphere packings'

Abstract

If it is made a condition that the volume of the arrangement be finite, the close sphere packings may be regarded as arrangements of objects having the largest possible separations between neighbours. In this case the arrangement of the centres is considered, and the assumptions of a spherical shape and of mutual contact are not necessary. The motives for applying this viewpoint in crystal chemistry, and its fruitfulness, are discussed. The paper aims at a plausible understanding of crystal structures and their metrics.